Abstract
The recently introduced multivariate multiscale entropy (MMSE) has been successfully used to quantify structural complexity in terms of nonlinear within- and cross-channel correlations as well as to reveal complex dynamical couplings and various degrees of synchronization over multiple scales in real-world multichannel data. However, the applicability of MMSE is limited by the coarse-graining process which defines scales, as it successively reduces the data length for each scale and thus yields inaccurate and undefined entropy estimates at higher scales and for short length data. To that cause, we propose the multivariate multiscale fuzzy entropy (MMFE) algorithm and demonstrate its superiority over the MMSE on both synthetic as well as real-world uterine electromyography (EMG) short duration signals. Based on MMFE features, an improvement in the classification accuracy of term-preterm deliveries was achieved, with a maximum area under the curve (AUC) value of 0.99.
Highlights
The concept of structural complexity [1,2,3] and the study of complex adaptive systems [4,5]spans a range of interdisciplinary approaches, from the theory of nonlinear dynamical systems to information theory, statistical mechanics, biology, sociology, ecology and economics [6,7]
We considered 10 scales for each epoch, so that the coarse graining process of multivariate multiscale fuzzy entropy (MMFE)/multivariate multiscale entropy (MMSE) analysis yielded only 120 samples at the highest scale, which was sufficient for MFSampEn calculation
To make a fair comparison between MMSE and MMFE in Table 1, only first 9 components were taken after applying principal component analysis(PCA) on the 10-element feature vectors which explained 100% variance in total
Summary
The concept of structural complexity [1,2,3] and the study of complex adaptive systems [4,5]. In (multivariate) sample entropy, the degree of similarity between any two delay vectors is based on a Heaviside function for which the boundary is rigid-the contributions of all data points inside the boundary are treated whereas the data points outside the boundary are ignored This principle is similar to a two-state classifier; the hard boundary causes discontinuity, which may lead to abrupt changes in entropy values even when the tolerance r is slightly changed, and sometimes it fails to find a SampEn value because no template match can be found for a small tolerance r.
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